Equivalent Definitions of A Closed Set
In a topological space, a set is closed if and only if it coincides with its closure. Equivalently, a set is closed if and only if it contains all of its limit points.
This is not to be confused with a closed manifold.
Read more about this topic: Closed Set
Famous quotes containing the words equivalent, definitions, closed and/or set:
“The notion that one will not survive a particular catastrophe is, in general terms, a comfort since it is equivalent to abolishing the catastrophe.”
—Iris Murdoch (b. 1919)
“Lord Byron is an exceedingly interesting person, and as such is it not to be regretted that he is a slave to the vilest and most vulgar prejudices, and as mad as the winds?
There have been many definitions of beauty in art. What is it? Beauty is what the untrained eyes consider abominable.”
—Edmond De Goncourt (1822–1896)
“The return of the asymmetrical Saturday was one of those small events that were interior, local, almost civic and which, in tranquil lives and closed societies, create a sort of national bond and become the favorite theme of conversation, of jokes and of stories exaggerated with pleasure: it would have been a ready- made seed for a legendary cycle, had any of us leanings toward the epic.”
—Marcel Proust (1871–1922)
“Scholarship cannot do without literature.... It needs literature to float it, to set it current, to authenticate it to all the race, to get it out of closets and into the brains of men who stir abroad.”
—Woodrow Wilson (1856–1924)